Question: The sum of two numbers is $111$, and their difference is $39$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 111}$ ${x-y = 39}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 150 $ $ x = \dfrac{150}{2} $ ${x = 75}$ Now that you know ${x = 75}$ , plug it back into $ {x+y = 111}$ to find $y$ ${(75)}{ + y = 111}$ ${y = 36}$ You can also plug ${x = 75}$ into $ {x-y = 39}$ and get the same answer for $y$ ${(75)}{ - y = 39}$ ${y = 36}$ Therefore, the larger number is $75$, and the smaller number is $36$.